Coupling of waveguides with very dissimilar mode field diameters (MFDs) is a critical problem of fiber-to-chip connectivity, when a single-mode optical fiber with MFD of ˜10 um has to be connected to a high-index waveguide with a sub-wavelength cross-section (e.g. a 0.2×0.5 um Si wire). Current solutions to coupling comprise, for example, butt coupling assisted by inverted taper, vertical coupling assisted by a diffraction grating; angle polished grating assisted coupling, a combination of butt coupling and evanescent coupling, evanescent coupling of the fiber core of a side polished fiber and a planar waveguide on a separate substrate (the side polished fiber and the planar waveguide are separate input/output ports). Problems of these approaches may include limited coupling efficiency (˜1.5 dB) and/or low mechanical strength. Thus, there is an long-standing and unresolved need for improved coupling with dissimilar MFDs.